A universal algorithm for Krull's theorem

Autor: Thomas Powell, Franziskus Wiesnet, Peter Schuster

Publikováno v: Powell, T, Schuster, P & Wiesnet, F 2022, ' A universal algorithm for Krull's theorem ', Information and Computation, vol. 287, 104761 . https://doi.org/10.1016/j.ic.2021.104761

We give a computational interpretation to an abstract formulation of Krull's theorem, by analysing its classical proof based on Zorn's lemma. Our approach is inspired by proof theory, and uses a form of update recursion to replace the existence of ma

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8a39525a2ed2eb9761de510ffd41041b
https://purehost.bath.ac.uk/ws/files/219876502/accepted_manuscript_nonformatted.pdf

Ideals and differential operators in the ring of polynomials of infinitely many variables

Autor: Miklós Laczkovich

Publikováno v: Periodica Mathematica Hungarica. 69:109-119

Let \(\Omega \) be an uncountable and algebraically closed field. We prove that every ideal of the polynomial ring \(R=\Omega [x_1 ,x_2 ,\ldots ]\) is the intersection of ideals of the form \(\{ f\in R: D(fg)(c)=0\) for every \(g\in R\}\), where \(D\

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::f2a21609fb0bcbdd65cd048c961dd89a
https://doi.org/10.1007/s10998-014-0059-7

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